# Logico Fractatus | Bad Fractals – Part 1

For a couple of months now, I’ve been involved in the work of deliberately creating some pretty Bad Fractals, as I call the project. Here, the goal, which is turning out swimmingly, is to find those “10000” solutions that won’t work,” to find and better by far those solutions, techniques, tricks, and tips that do to make better images. Here I have three images, two Bad, progressively less so, before reaching the third, and final image of the set. So, I’ll comment on each, and discuss what I like and don’t like about it, and why I think the Bad Fractals are just that. The images below are all courtesy of Fractal Domains for Mac. Let’s start with the first, and the worst of these! This post’s images use a modified Newton’s Method fractal type, and I’ve added terms to the formula’s numerator with higher exponent values. Bad Fractals in this series use 800 x 450 pixel resolution unless otherwise indicated:

I have serious problems with this one. While the pixelation with this could be corrected, the real issue here is the color maps used, both in the orbit traps and the fixed points. In short, this one’s colors are far too busy. In the orbit traps they bleed into each other and spoil the image’s detail, blurring the definition of the orbit traps and so spoiling the esthetics of the piece. The fixed points outside the orbit traps are too garish for my tastes. I attempt to fix those issues with the image just below, but even this has problems . . . .

This one is a bit worrisome too, even with the color maps adjusted. One, the color map of the fixed points clashes with that of the orbit traps, and two, the orbit traps are split by the orbits of the fractal set, which means I have to define the color map for each orbit region. I have improved things a bit here by lowering the range of colors available for color randomization, my usual method before adjusting color maps manually, so what appears immediately above isn’t that busy. Still, even with a reduced range of colors involved, the mismatch between the earthy shades of the fixed points and the more floral-looking orbit traps becomes apparent. So let’s try for something that doesn’t clash so much:

This one is a reasonably full-sized 1600 x 900 wallpaper, so the pixelation isn’t nearly as problematic. I’ve finally got the image to something a bit less Bad, just a wee bit, because I fixed the color map problems and the orbit trap settings of the previous two. This one had a maximum color map selection by use of randomizing somewhere between 9 and 12, and a minimum of 2, and this greatly improved the colors of the first. This one is much better even than the second in that there was no region-splitting for the orbit traps with the colors I got, so those don’t look out of place with the maps for the fixed points. The colors for traps and points fit much better together here, as I took more time selecting a better match for each. I think that this one seems a better image as a result, but you be the judge using your own sense of taste, not mine!

Tf. Tk. Tts.

# Logico Fractatus | New Wallpapers – 2017.10.24

This time, I have two new images courtesy of Fractal Domains, the very first fractal program I’ve ever used, and luckily can still use on the new laptop. These are among the better outcomes of my Bad Fractals ongoing project. Why Bad Fractals? The goal here is to find grunchloads of fractal making solutions that don’t work, to isolate and point out the ones that do, and thereby create better images in the process. Feel free to use these images if you wish for any non-commercial purposes, just leave a link to the original post or mention of the source when you do! Thanks, and enjoy!

Tf. Tk. Tts.

# Logico Fractatus | Gnarly, Dude!

I’m currently creating Bad Fractals to go into the folder of the same name, for all of my really awful images created over the years. The method behind that madness involves working backward from the Bad images to discover insights into drastically improving the more passable ones, to discover those “10,000 solutions that don’t work,” and to better the ones that do. I’m saving the parameter sets for each new Bad Fractal created, and in between, I’m also creating those that may not be quite as Bad. One of those is tonight’s image, created by MB3D, using the Gnarl formula type and transparency settings. The image links to the fractal’s page in my DeviantArt gallery. Enjoy!

Tf. Tk. Tts.

# Fractals of the Week | I’ve Got Newton on ‘Dis!

This week, I feature images using the math of a certain cranky English guy, responsible for the Laws of Motion, and those Harry Potter-esque alchemical experiments in his attic, trying to convert base metals into gold, and create the Sorcerer’s, er, I mean Philosopher’s Stone. These pieces, a couple released for the first time on this blog, also use symmetry transformations, or mapping, from a range of mathematicians, including one (#2) whose work has been featured before, Felix Klein. Regardless of their origination, these were fun to play with, and will be followed by more in future.

Each of the full-sized images measures 1600×900 pixels, so feel free to double-click for complete ginormification.

Tf. Tk. Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

# Fractal of the Week | Brains in Spaaace!

Namaskar. I’ve been busy with study, working on notes, and creating new presets for MB3d now that I’ve finished resizing older ones to economize on file space, and this so far is my favorite of the bunch. It’s a truly alien-looking object that I’ve rendered as a 1600×900 wallpaper. This seems a good starting point for a larger print-sized image. I’m keeping this one’s basic preset with fewer edits than I thought might be needed during this first render shown here. Double-click to embiggen.

Boltzmann

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

# Fractals of the Week | Newton’s Bounty, So Passing Strange

Here I’ve a few wallpapers from a parameter set using Fractal Domains as an example of how useful older apps can remain. I’ve still not found a version of the Mandelbulber app that will work with my current OS, El Capitan, so I’m forced to find new methods with apps that may seem at first more limited. FD is the first app I ever used, and the most limited. FD uses only 4 fractal types; Newton, Halley, Mandelbrot set (and its corresponding Julia sets), and a more generalized Mandelbrot set, kinda, sorta, using a method of finding ratios which allows more variation in formula exponents, like z^3, z^4, and so on, instead of only z^2 as with the regular M-set. These are all created from the same Newton fractal parameter set, and vary by far in differences in the formula numerator.

Small changes can have a big effect! Double-click to macro-transscalify each image to full size!

Tf.Tk.Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

# Fractal of the Week | Newton’s Waking

This is one of my more recent forays into using a different formula numerator for Newton’s method fractals. I’ve lately been looking into improving some of my better-looking, or perhaps less odious, early images for larger file sizes suitable for use as prints.

The title of this piece derives from a term used as an objection to early modern science in a poem written by William Blake, the phrase ‘Newton’s sleep’ where the Newtonian worldview was decried as being somehow deadening to the human spirit or ‘soul.’ I propose instead that science as it was then, and as it is today can do much to advance the human spirit without saddling the same with metaphysical baggage or unverifiable concepts.

As a skeptic, I don’t deny the soul, but instead define it as the complete pattern of information making up a human being, or any other living thing capable of self-awareness, of the same substance as the brain and body. At the very least, it avoids frivolously multiplying concepts, and still manages perfectly well to explain human thought and behavior.

The math used to generate all of my work is unequivocally the product of science, which in turn derives from philosophy. Newton described himself as a natural philosopher as the term ‘scientist’ wasn’t coined until the 19th century. Hence, “Newton’s Waking.”

I’m still tweaking the preset that gave rise to this piece, and will post some of the more interesting examples here in future installments.

Tf. Tk. Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!